1. Field
The present disclosure relates to a method and apparatus for reconstructing an X-ray CT (computerized tomography) image, and more particularly, to a method and apparatus for reconstructing an X-ray CT image having high resolution locally.
2. Discussion of the Related Technology
When X-rays pass through an object, they show a property by which the intensity thereof decreases according to the physical property and length of the object. The property of the X-rays is described by “Lambert-Beer's Law” that is expressed as the following equation:I=I0e−μL   (1)
where I0 is the initial intensity of X-rays, μ is a unique X-ray attenuation coefficient of an object, and L is the length of the object through which the X-rays pass. This equation shows a relationship in which upon irradiation of X-rays with an initial intensity of I0, the X-rays are attenuated according to the attenuation coefficient and distance of the object through which the X-rays pass. This equation is applied to a case where the object comprises a single substance. In case of an object with a variety of substances mixed therein, the following equation is applied thereto:
                    I        =                              I            0                    ⁢                      ⅇ                          -                                                ∫                  0                  L                                ⁢                                                      μ                    ⁡                                          (                      s                      )                                                        ⁢                                                                          ⁢                                      ⅆ                    s                                                                                                          (        2        )            
where s is a path of X-rays, and μ(s) is an X-ray attenuation coefficient and is a function of a path since it varies according to locations in an object.
An X-ray system, which has been widely used for a nondestructive inspection for diagnosing the interior of a human body or finding a defect within an object, obtains a projection image by catching the intensity of X-rays, which varies according to locations on an object though which the X-rays pass, on a two-dimensional film. When X-rays pass through an object, the intensity of the X-rays varies according to the unique attenuation coefficient of the object and the path on which the X-rays travel, as expressed by the equations. The varying values are detected by a photosensitive film. Since such an X-ray projection photograph represents a final cumulative value obtained during passage of X-rays on a path within an object, it shows information on the interior of the object but has a disadvantage in that it cannot show information on the depth of the object, i.e., cross-sectional images.
On the contrary, an apparatus for reconstructing an X-ray CT image obtains several ten to several hundred projection images at various angles by rotating an object through 360 degrees or rotating an X-ray generator and a detector through 360 degrees around an object, and mathematically reconstructs the images using a computer to create information on the depth of the object, i.e., cross-sectional images. FIG. 1 is a schematic view illustrating an operational principle of an exemplary apparatus for reconstructing an X-ray CT image. The exemplary apparatus for reconstructing an X-ray CT image is configured to reconstruct CT images by rotating an X-ray generator 10 and an X-ray detector 20, which are installed to be spaced apart from a target object 11 of which CT images will be obtained and to face the target object, through 360 degrees around the target object 11, by generating X-rays 12 from the X-ray generator 10 at a predetermined angular interval, and by causing the X-ray detector 20 to detect the X-rays 12 that have passed through the target object 11. The most general method for creating cross-sectional images from data detected by the X-ray detector 20 is a back projection method, and its associated equations are as follows:
                              μ          ⁡                      (                          x              ,              y                        )                          =                              1            2                    ⁢                                    ∫              0                              2                ⁢                π                                      ⁢                                          ∫                                                      -                                          1                      2                                                        ⁢                                      t                    m                                                                                        1                    2                                    ⁢                                      t                    m                                                              ⁢                                                                    P                    θ                                    ⁡                                      (                    t                    )                                                  ⁢                                  h                  ⁡                                      (                                                                  x                        ⁢                                                                                                  ⁢                        cos                        ⁢                                                                                                  ⁢                        θ                                            +                                              y                        ⁢                                                                                                  ⁢                        sin                        ⁢                                                                                                  ⁢                        θ                                            -                      t                                        )                                                  ⁢                                  ⅆ                  t                                ⁢                                  ⅆ                  θ                                                                                        (        3        )                                                      P            θ                    ⁡                      (            t            )                          =                                            -              log                        ⁢                                                  ⁢                          I                              I                0                                              =                                    ∫              0                              L                ⁡                                  (                  t                  )                                                      ⁢                                          μ                ⁡                                  (                                      s                    ,                    t                                    )                                            ⁢                              ⅆ                s                                                                        (        4        )            
where θ and t are geometric conditions for acquisition of projection data and indicate a rotational angle and coordinates along the length of the X-ray detector 20, respectively, and tm is the total length of the detector 20. Pθ(t) is projection data obtained in the direction of θ. The function h(xcosθ+ysinθ−t) indicates a back projection filtering function. Generally, a Ram-Lak filter, a Shepp-Logan or the like is widely used. A function μ(x,y) that is desired to be obtained through calculation of such a back projection process is an attenuation coefficient at each of locations of a target object, which represents how much X-rays are attenuated upon passage thereof through the object. The function means desired cross-sectional images. Consequently, the apparatus for reconstructing an X-ray CT image quantitatively calculates unique attenuation coefficients at respective locations according to the kind of object when X-rays pass through cross sections of an object, and shows the calculated results as images.
FIG. 2 is a schematic view showing a basic configuration of an apparatus for reconstructing an X-ray CT image, which is mainly used at present. As shown in FIG. 2, the exemplary apparatus for reconstructing an X-ray CT image has an X-ray generator 10 and an X-ray detector 20, which are secured on a rotatably installed gantry 30. The X-ray generator 10 and the X-ray detector 20 are fixedly installed at opposite positions with respect to a rotational center of the gantry 30 such that they are equidistantly spaced apart from the rotational center. An X-ray detector 20 of an early apparatus for reconstructing a CT image is constructed in a one-dimensional arrangement in the form of a line to mainly obtain two-dimensional cross-sectional images. Recently, with the development of hardware technology, the X-ray detector 20 is developed from the one-dimensional arrangement in the form of a line to a limited two-dimensional arrangement in the form of several to several tens of lines. Thus, an obtained image is developed to a limited three-dimensional image. Further, there is a recent tendency for an X-ray detector to be gradually developed to a complete two-dimensional arrangement.
The resolution R of a cross-sectional image obtained by the apparatus for reconstructing an X-ray CT image constructed as above is determined according to a relative ratio of the distance from the X-ray generator 10 to the X-ray detector 20, i.e., a source to detector distance (SD), and the distance from the X-ray generator 10 to the center of a target object 11, i.e., a source to object distance (SOD). The resolution R can be expressed as the following equation. Here, “DS” is a pixel size of the X-ray detector 20.
                    R        =                              S            ⁢                                                  ⁢            O            ⁢                                                  ⁢            D            ×            D            ⁢                                                  ⁢            S                                S            ⁢                                                  ⁢            D                                              (        5        )            
In the exemplary apparatus for reconstructing an X-ray CT image, an X-ray detector with a fixed pixel size is used, the distance between the X-ray generator and the X-ray detector is fixed, and the center of a target object is placed at the center between the X-ray generator and the X-ray detector. Therefore, the exemplary apparatus for reconstructing an X-ray CT image always provides only a cross-sectional image with a fixed pixel size.
To obtain a high resolution cross-sectional image using the apparatus for reconstructing a CT image with a fixed pixel size, it is possible to utilize magnification effects that are obtained by moving the target object toward the X-ray generator to obtain a cross-sectional image. As shown in FIG. 3, the magnification effects refer to effects by which the resolution of data projected on the X-ray detector is improved since X-rays 12 passing through the interior of the target object 11 placed close to the X-ray generator 10 are denser than those passing through the interior of the target object 11 placed close to the X-ray detector 20. That is, a portion of the target object is placed close to the X-ray detector and thus is magnified and projected on the X-ray detector, thereby improving the resolution.
However, there is a problem in that the movement of the target object toward the X-ray generator for improving the resolution through the magnification effects causes a portion of the target object to deviate from a range of irradiation angles between the X-ray generator and the X-ray detector. Basically, in a method for reconstructing a CT image, the entire target object of which an image is to be reconstructed should be included in the range of irradiation angles of X-rays between the X-ray generator and the X-ray detector. Therefore, if a portion of the target object 11 deviates from the range of irradiation angles of X-rays as shown in FIG. 3, projection data acquired by the X-ray detector 20 do not include projection data on the portion of the target object that deviates from the range of irradiation angles, so that a complete cross-sectional image cannot be reconstructed. Accordingly, if it is intended to obtain a high resolution cross-sectional image using the magnification effects, there is a problem in that a target object is limited to a small target object which can be fully included in a range of irradiation angles of X-rays even though the target object is placed close to an X-ray generator. This problem is common to both an apparatus with a fan-beam X-ray generator and an apparatus with a cone-beam X-ray generator if it is intended to improve the resolution of a cross-sectional image using the magnification effects.
Meanwhile, U.S. Pat. No. 6,246,742 entitled “Local CT image reconstruction with limited x-ray exposure” discloses a method for obtaining a CT image by locally exposing only a desired portion of a target object to X-rays while controlling an irradiation angle of X-rays of an X-ray generator so that a CT image for the portion exposed to the X-rays can be obtained. However, as for the resolution of a local CT image obtained by means of the method disclosed in the patent, the CT image is a cross-sectional image with a resolution predetermined upon manufacture of an apparatus. It is not possible to obtain a local high resolution CT image.
There is a case where a local high resolution CT image is required for an accurate diagnosis of a specific part of a patient or clinical study. However, as discussed above, all the exemplary apparatuses for reconstructing an X-ray CT image have limitations in that they can provide only a cross-sectional image with a resolution predetermined upon manufacture of the apparatuses and thus cannot provide a local cross-sectional image with a proper resolution as desired.
The foregoing discussion is to provide general background information, and does not constitute an admission of the prior art.